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Abstract

Microcoil resonators are a radical new geometry for high Q resonators with unique linear features. In this paper I briefly summarise their linear properties before extending the analysis to nonlinear interactions in microcoil resonators. As expected such nonlinear resonators are bistable and exhibit hysteresis. Finally I discuss possible applications and extensions to such resonators.

It should be noted that there are at least two misprints in Sumetsky’s Optics Express paper [2]. Firstly in Eq. 1 there is a factor i missing on the L.H.S. Secondly in the equation for the transmission a factor of exp(iβl) is missing. Both of these misprints do not occur in his original paper.

Other (3)

It should be noted that there are at least two misprints in Sumetsky’s Optics Express paper [2]. Firstly in Eq. 1 there is a factor i missing on the L.H.S. Secondly in the equation for the transmission a factor of exp(iβl) is missing. Both of these misprints do not occur in his original paper.

Figures (3)

(a) Schematic of a microcoil resonator taken from [2]. (b) Transmission spectrum for a lossy OMR with 8 coils. The loss is 0.02dB/mm while the coupling strength was 3mm-1. The green line shows the expected transmission for a straight length of fibre with the same length and loss.

Normalised group velocity (top row) and dispersion (bottom) for a 8 turn OMR with the same parameters as the one shown in Fig. 1. The figures on the right are expanded versions of the main graphs showing the narrow wavelength region of negative group velocity. Note that off resonance the dispersion is still large (1000’s of picoseconds squared) and increases by several orders of magnitude on resonance. In the graphs the spikes are due to numerical errors at points where the group velocity becomes undefined.

Nonlinear response of a 3 turn microcoil resonator. Fig. (a) shows the full solution (both stable and unstable branches) as a function of the input power. Fig. (b) shows the output phase while Fig. (c) shows the hysteresis curves for the resonator for a range of wave-lengths. Figyre 3(a) shows the transmission as a function of the normalised input power for a wavelength of λ=1.53022µm. This is on the long wavelength size of the resonance and so one would expect the transmission to decrease as the intensity increases as can be seen. It is also clear that there is a wide range of intensities over which the transmission is no longer single valued and thus one expects the system to exhibit bistability and hysteresis. In this case the maximum contrast between the high and low transmission branches is > 33dB. The limiting factor in the contrast ratio is the fact that as the loss increases the signal intensity drops to the point where the transmission is linear thus reducing the loss. Figure 3(b) shows the output phase as a function of the input intensity and is discussed further in the appendix.